Michael Bloomberg, already waist-deep in a heated mayoral campaign, waded into a fresh political fight yesterday after saying he would work as a “third senator” for New York.

Bloomberg said that because both New York senators, Charles Schumer and Hillary Rodham Clinton, are Democrats, he would try to use the mayor’s office to lobby for increased federal funding from the Republican Bush administration.

“I’ve got to go and represent New York City in Washington and get the help from there,” the Republican hopeful said in an interview on radio station WABC. “We don’t get our fair share . . . I’ve got to be, as mayor, the third senator, if you will.”

In a nod to the state’s already-elected representatives in Washington, Bloomberg said Clinton, Schumer and Rep. Charles Rangel (D-Manhattan) “can help” in his effort to get greater funding.

Clinton responded to Bloomberg’s offer of “help” with a civics and history lesson for the billionaire media mogul.

“I think our founders had a pretty good framework when they set up the Senate, and we have two senators for each state,” said Clinton. “I’ll wait and see who’s actually mayor, and I expect it will be one of the Democratic candidates.”

“This election is about choosing a mayor, not an amateur ambassador to the Bush-Cheney White House.”

City Comptroller Alan Hevesi also lambasted the Republican hopeful, noting that Bloomberg already has spent $8 million on his campaign. “Billionaire Bloomberg is spending so much money, he’s trying to buy two offices at once,” scoffed Hevesi spokesman Josh Isay. “Another 10 million and he’ll be saying he’s going to be our second governor and second president.”

Fernando Ferrer adviser John Del Cecato said Bloomberg “seems confused” – especially since he said just a few weeks ago that the Bronx borough president was wrong to speak out on immigration law because it is a federal, not a city, issue.

“Now, Mr. Bloomberg pines to be a player in Washington,” Del Cecato said. “It’s a head-scratcher.”

Bloomberg’s rival for the Republican party nod, Herman Badillo, said his opponent is trying to attach himself to Bush in an effort to “[look] for credibility, because his credibility is sinking every day.”

The Bloomberg campaign defended the “third senator” strategy.

“How anyone could be against New York City getting its fair share of federal and state funds is a total mystery,” said spokesman Ed Skyler.

The contretemps came days after Bloomberg raised eyebrows by saying he favors a form of prayer in school – even the Lord’s Prayer – although he would not fight for such a change as mayor.